Functional completeness of planar Rydberg blockade structures

TL;DR

This paper demonstrates that planar Rydberg atom structures can realize any constrained Hilbert space, enabling the simulation of complex quantum phases and topological models through minimal logic primitives.

Contribution

It introduces a framework and minimal primitives for constructing any local constraint Hilbert space using planar Rydberg atom arrangements.

Findings

Realized string-net Hilbert spaces with Rydberg atoms

Proved the functional completeness of planar Rydberg structures

Discussed optimization strategies for robustness

Abstract

The construction of Hilbert spaces that are characterized by local constraints as the low-energy sectors of microscopic models is an important step towards the realization of a wide range of quantum phases with long-range entanglement and emergent gauge fields. Here we show that planar structures of trapped atoms in the Rydberg blockade regime are functionally complete: Their ground state manifold can realize any Hilbert space that can be characterized by local constraints in the product basis. We introduce a versatile framework, together with a set of provably minimal logic primitives as building blocks, to implement these constraints. As examples, we present lattice realizations of the string-net Hilbert spaces that underlie the surface code and the Fibonacci anyon model. We discuss possible optimizations of planar Rydberg structures to increase their geometrical robustness.